Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily homework quiz will be given at the end of class.

Writing Linear Equations 2 Section 8.1

Review of formulas covered in Chapter 3:

Note: You can use a printed copy of the sheet containing formulas on quizzes/tests. Yellow handout copies for you to keep are available here and in the open lab. ( You can also view/print a copy of the formula sheet online by clicking on the “Formula sheet” menu button.) Keep a copy of this sheet in your notebook to use while you do your homework assignments and practice quizzes/tests so you know which ones will be available to you on the sheet and where to find them. Clean copies will be handed out for your use at each quiz/test, so you may write notes on your own copy, but you won’t have those notes available as you take the quiz in class.

Find the equation of the line through (-4,0) and (6,-1). Write the equation in standard form. First find the slope. Last session we applied the point-slope formula to problems in which we were given the slope and one point on the line. Example: What if we’re given TWO POINTS on the line? Today we’ll be applying the point-slope formula to problems with different sets of information:

Example (cont.) Now substitute the slope and either one of the points into the point-slope formula. For standard form, clear fractions by multiplying both sides by 10. (use distributive property) (add x to both sides) (This would give but we need standard form.)

Problem from today’s homework: Answer in slope-intercept form: y = -1/3x +10/3 Answer in standard form: x + 3y = 10

Nonvertical parallel lines have identical slopes. Nonvertical perpendicular lines have slopes that are negative reciprocals of each other. Remember: If you rewrite linear equations into slope-intercept form (i.e. solve for y), you can easily determine the slope. Quick review: parallel and perpendicular lines

Find an equation of a line that contains the point (3,-5) and is perpendicular to the line 3x + 2y = 7. Write the equation in slope-intercept form. First, we need to find the slope of the given line. 2y = -3x + 7 (subtract 3x from both sides) Example (divide both sides by 2) Since perpendicular lines have slopes that are negative reciprocals of each other, we use the slope of 2/3 for our new equation, together with the given point (3,-5).

Example (cont.) (multiply by 3 to clear fractions) (use distributive property) (subtract 15 from both sides) (divide both sides by 3) (simplify)

First, we need to find the slope of the given line. 3y = -x + 6 (subtract x from both sides) Example: y = x + 2 (divide both sides by 3) Since parallel lines have the same slope, we use the slope of for our new equation, together with the given point. Find an equation of a line that contains the point (-2,4) and is parallel to the line x + 3y = 6. Write the equation in standard form.

(multiply by 3 to clear fractions) (use distributive property) (add x to both sides) (Why? Because they want it in STANDARD form) (add 12 to both sides) Example (cont.) What would this look like in slope-intercept form?

Find the equation of the line parallel to y = -4, passing through the point (0,-3). The line y = -4 is a horizontal line (slope = 0). If the new line is parallel to this horizontal line y = -4, then it must also be a horizontal line. So we use the y-coordinate of our point to find that the equation of the line is y = -3. NOTE: Sketching a quick graph of the line y = -4 and the point (0,-3) can help you visualize the situation and make sure you are solving the problem correctly. Example:

Find the equation of the line perpendicular to x = 7, passing through the point (-5,0). The line x = 7 is a vertical line. If the new line is perpendicular to the vertical line x = 7, then it must be a horizontal line. So we use the y-coordinate of our point to find that the equation of the line is y = 0. Again: Sketching a quick graph of the line x = 7 and the point (-5,0) can help you visualize the situation and make sure you are solving the problem correctly. Example

Application problems that involve figuring out the equation of a line:

The assignment on this material (HW 8.1) Is due at the start of the next class session. Lab hours: Mondays through Thursdays 8:00 a.m. to 7:30 p.m.

You may now OPEN your LAPTOPS and begin working on the homework assignment until it’s time to take the quiz on HW 3.5.

Please open your laptops, log in to the MyMathLab course web site, and open Quiz 3.5. IMPORTANT NOTE: If you have time left after you finish the problems on this quiz, use it to check your answers before you submit the quiz! Remember to turn in your answer sheet to the TA when the quiz time is up. You will have access to the online calculator on your laptop during this quiz. No other calculator may be used.